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It is well known that the linear theory of collisionless damping breaks down after a time τ ≡ (m/eεκ)½, where κ is the wavenumber and ε is the amplitude of the electric field. Jacobi elliptic functions are now used to provide an exact solution of the Vlasov equation for the resonant electrons, and the damping coefficient is generalized to be valid for times greater than t = τ. This generalized damping coefficient reduces to Landau's result when t/τ ≪ 1; it has an oscillatory behavior when t/τ is of order unity, and it phase mixes to zero as t/τ approaches infinity. The above results are all shown to have simple physical interpretations.

Recently, a simple model was proposed for the nonlinear interaction of a low-density monoenergetic electron beam and a relatively cold infinite homogeneous one-dimensional plasma. The essential feature of this model is the observation that after several e-foldings the bandwidth of the growing waves is so narrow that the electrons interact with a very nearly pure sinusoidal field. In terms of this single wave model, a properly scaled solution of the nonlinear beam-plasma problem which depends analytically on all the basic parameters of the problem (i.e., plasma density, beam density, plasma thermal velocity, and beam drift velocity) is presented. This solution shows that the single wave grows exponentially at the linear growth rate until the beam electrons are trapped. At that time the wave amplitude stops growing and begins to oscillate about a mean value. During the trapping process the beam electrons are bunched in space and a power spectrum of the higher harmonics of the electric field is produced. Both the oscillation in wave amplitude and the power spectrum are given a simple physical interpretation.

The inviscid damping of an asymmetric perturbation on a two-dimensional circular vortex is examined theoretically, and with an electron plasma experiment. In the experiment, an elliptical perturbation is created by an external impulse. After the impulse, the ellipticity ͑quadrupole moment͒ of the vortex exhibits an early stage of exponential decay. The measured decay rate is in good agreement with theory, in which the perturbation is governed by the linearized Euler equations. Often, the exponential decay of ellipticity is slow compared to a vortex rotation period, due to the excitation of a quasimode. A quasimode is a vorticity perturbation that behaves like a single azimuthally propagating wave, which is weakly damped by a resonant interaction with corotating fluid. Analytically, the quasimode appears as a wave packet of undamped continuum modes, with a sharply peaked frequency spectrum, and it decays through interference as the modes disperse. When the exponential decay rate of ellipticity is comparable to the vortex rotation frequency, the vorticity perturbation does not resemble a quasimode; rather, it is rapidly dominated by spiral filaments. Over longer times, linear theory predicts algebraic decay of ellipticity; however, nonlinear oscillations of ellipticity emerge in the experiment before a transition to algebraic decay would occur.

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In recent experiments ultracold plasmas were produced by photoionizing small clouds of laser cooled atoms. This paper presents the results of molecular dynamic simulations for the early time evolution of such plasmas. Contrary to earlier speculation, no evidence of strong electron–electron correlations is observed in the simulations even if the initial value of the coupling parameter (Γe=e2/akTe) is much larger than unity. As electron–electron correlations begin to develop, the correlation energy is released to heat the electrons, raising the electron temperature to the point where Γe∼1 and limiting further development of correlation. Further heating of the electrons occurs as a by-product of three-body recombination. When a model of laser cooling is added to the simulation, the formation of strong ion–ion correlation is observed. Contrary to earlier suggestion, the rate of three-body recombination is observed to be in reasonable agreement with the traditional formula, R=3.9×10−9 s−1[n(cm−3)]2[Te(K)]−9/2, but care must be taken to use the correct temporally evolving temperature, Te. The simulations are challenging because it is necessary to follow three-body recombination into weakly bound (high n quasiclassical) Rydberg states, and the time scale for such states is short compared to that for the plasma dynamics. This kind of problem was faced earlier in computational astrophysics when studying binary star formation in globular clusters and the simulation method used here is adapted from such studies.

The three-body recombination rate is calculated for an ion introduced into a magnetically confined, weakly correlated, and cryogenic pure electron plasma. The plasma is strongly magnetized in the sense that the cyclotron radius for an electron rce=(kBTe/me)1/2/Ωce is small compared to the classical distance of closest approach b=e2/kBTe, where Te is the electron temperature and Ωce=eB/mec is the electron cyclotron frequency. Since the recombination rate is controlled by a kinetic bottleneck a few kBTe below ionization, the rate may be determined by considering only the initial cascade through states of electron-ion pairs with separation of order b. These pairs may be described as guiding center atoms since the dynamics is classical and treatable with the guiding center drift approximation. In this paper, an ensemble of plasmas characterized by guiding center electrons and stationary ions is described with the BBGKY hierarchy. Under the assumption of weak electron correlation, the hierarchy is reduced to a master equation. Insight to the physics of the recombination process is obtained from the variational theory of reaction rates and from an approximate Fokker–Planck analysis. The master equation is solved numerically using a Monte Carlo simulation, and the recombination rate is determined to be 0.070(10)n2eveb5 per ion, where ne is the electron density and ve=(kBTe/me)1/2 is the thermal velocity. Also determined by the numerical simulation is the transient evolution of the distribution function from a depleted potential well about the ion to its steady state.

We apply "rotating wall" electric fields to spin up a non-neutral plasma in a Penning-Malmberg trap, resulting in steady-state confinement (weeks) of up to 10 9 Mg 1 ions. The resulting ion columns can be near global thermal equilibrium, with near-uniform temperature and rotation frequency. The equilibrated plasma E 3 B rotation rate f E is observed to be somewhat less than the drive frequency f w , with slip Df ϵ f w 2 f E depending on temperature as Df~T 1͞2 for 0.05 & T & 5 eV. Dynamic measurements of applied torque versus slip frequency show plasma spin up and compression for Df. 0 and plasma slowing and expansion for Df , 0. By gradually increasing f w , density compression up to 20% of the Brillouin density limit has been achieved. Heating resonances and hysteresis in plasma parameters are also observed.